2.8 beta won't let me texture-paint on bump map slot interactively
I found the answer to my problem, with some prodding from @CraigDJones:  there's two things that enable texture bump painting to work as I expect:


Use LookDev preview mode in the 3D View texture painter
Turn off the Overlays.


It's not clear why either of these steps are required, but for this beta at least (2019-02-10 Windows version) I've got a functioning solution.

==== EDIT ====

Sadly, that solution only works for very simple .blend files, it seems.  I have a more complex model and I still cannot get texture painting to work on the bigger model.  It seems like there are so many weaknesses from a UX perspective in this feature that it just can't be called a 'feature' yet. :(

I've had to un-accept my own answer: there's a novelty!